Method for measuring polarization dependent loss and insertion loss

ABSTRACT

This invention provides a method of obtaining accurate measurements of polarization dependent loss and insertion loss during the tests aiming at measuring the polarization properties of optical components. This is achieved by taking into account every polarization disturbance in the line between generation of known states of polarization and the device under test. The method involves computing within a desired range of wavelengths either the transfer matrix of each polarization perturbing element or of all polarization perturbing elements as a whole, and compensating for errors introduced by these polarization perturbing elements.

FIELD OF THE INVENTION

[0001] This invention relates to a method for accurately measuringpolarization dependent loss (PDL) and insertion loss (IL). Morespecifically, it relates to a method for compensating the polarizationerrors introduced during the tests aiming at measuring the polarizationproperties of optical components. In particular, it relates to a methodthat compensates for perturbations of the states of polarizationoccurring in the line between the generation of input polarizations andthe device under test (DUT).

BACKGROUND OF THE INVENTION

[0002] The performance of a fiber optic system is assessed throughvarious parameters, such as insertion loss (IL), polarisation dependentloss (PDL) and polarization mode dispersion (PMD). Among the few methodsknown to calculate the PDL, the method of using the Mueller matrix makespossible accurate and rapid measurements. It consists in launching fourdifferent orthogonal states of polarization to a DUT. The measurement ofthe optical power transmitted in these four polarization states enablesthe calculation of the PDL of the component. One application of themethod is disclosed in U.S. Pat. No. 5,371,597.

[0003] As is known, for determining the PDL and the IL, a polarizationcontroller is needed to generate four orthogonal states of polarization.The polarization controller typically comprises a polarizer andfractional-wave plates, also referred to as retardation plates orbirefringent plates or phase shifters. The polarizer insures a constantlinear input polarization;

[0004] The fractional-wave plates are orientated so as to obtain desiredpolarization states. Knowing the input signal by its Stokes vectorS_(ij in) each state of polarization, the Stokes vector S_(ij out) ofthe output signal is obtained by multiplication using the Mueller matrixm_(ij). To determine the PDL and IL, the only terms that one needs toobtain are those of the top row of the Mueller matrix (m_(ij)).

OBJECTS AND SUMMARY OF THE INVENTION

[0005] It is an object of the present invention to provide an improvedmethod for accurately measuring PDL and IL by compensating for thepolarization errors introduced during such measurement.

[0006] Another object is to provide a method that allows accurate PDLand IL measurements within a range of wavelengths.

[0007] Still another object is to provide a method that allowssimultaneous measurements of several devices with accuracy.

[0008] Other objects and advantages of the invention will be apparentfrom the following description thereof.

[0009] Normally, to obtain the PDL and the IL of the DUT, four scanningsare carried out successively with four orthogonal polarization states onthe Poincaré sphere. Polarizations thus generated by the polarizationcontroller are, for instance, the horizontal linear polarization, thelinear vertical polarization, the linear polarization at 45° and theright-hand circular polarization.

[0010] In matrix formalism, the transfer matrix of the DUT, referred toa relates the output polarization matrix |S_(ij out)| measured for thesefour independent input states of polarization represented by matrix|S_(ij in)| according to the following equation;

|S _(ij out) |=|m _(ij) ||S _(ij in) |  (1)

[0011] With known input polarizations (|S_(ij in)|), the measurement atthe output (|S_(ij out)|) is sufficient to determine the transfer orMueller matrix of the DUT by resolution of a system of equations. Theinfluence on transmission depending of incident polarization (PDL) iscontained in the 4 terms of the top row of the Mueller matrix$\begin{bmatrix}S_{11\quad {out}} & S_{12\quad {out}} & S_{13\quad {out}} & S_{14\quad {out}} \\. & . & . & . \\. & {.S_{{ij}\quad {out}}} & . & . \\. & \ldots & . & .\end{bmatrix} = {\quad\left\lbrack {\left. \quad\begin{matrix}m_{11} & m_{12} & m_{13} & m_{14} \\. & . & . & . \\. & m_{ij} & . & . \\. & . & . & .\end{matrix} \right\rbrack \cdot {\quad\begin{bmatrix}S_{11\quad {in}} & S_{12\quad {in}} & S_{13\quad {in}} & S_{14\quad {in}} \\S_{21\quad {in}} & S_{22\quad {in}} & S_{23\quad {in}} & S_{24\quad {in}} \\S_{31\quad {in}} & S_{32\quad {in}} & S_{33\quad {in}} & S_{34\quad {in}} \\S_{41\quad {in}} & S_{42\quad {in}} & S_{43\quad {in}} & S_{44\quad {in}}\end{bmatrix}}} \right.}$

[0012] where the S_(1j out) are powers measured at the output and theS_(ij in), with i=1, 2, 3, 4 the matrix row index and j=1, 2, 3, 4 thematrix column index, characterize the input polarizations.

[0013] Once these elements m_(ij) are computed, the transmissioncoefficients t_(j) defined as the measured power, referred to as Mes,which is the power transmitted measured at the output of the DUTcompared to the reference power, referred to as Ref, which is the powerin absence of the DUT, are obtained as functions of said elements m_(ij)of the top row of the Mueller matrix:

t _(j) =S _(1j out) /S _(1j in) =Mes(j)/Ref(j)=f(m _(ij))

[0014] In particular, in the case of four orthogonal polarization stateson the Poincaré sphere such as the linear vertical polarization, thelinear polarization at 45° and the right-hand circular polarization, thefour elements m_(ij) of the top row of the Mueller matrix are obtainedas:

[0015] m₁₁=½(t₁+t₂) m₁₂½(t₁−t₂) m₁₃=(t₃−m₁₁) m₁₄=(t₄−m₁₁)

[0016] In any case, the PDL and the IL are calculated according to thefollowing equations: $\begin{matrix}{{PDL} = {10\quad \log \frac{t_{\max}}{t_{\min}}\left( {B} \right)}} & (2)\end{matrix}$

IL=10 log_(M) ₁₁   (3)

[0017] where the t_(max) and t_(min), are the maximum and minimumtransmissions respectively, defined for any four independent states ofpolarization according to the following relations:

t _(max) =m ₁₁ +{square root}{square root over (m₁₂ ²+m₁₃ ²+M₁₄ ²)}  (4)

t_(min)=m₁₁−{square root}{square root over (m₁₂ ² m ₁₃ ² m ₁₄ ²)}  (5)

[0018] To generate the four desired states of polarization, a typicalpolarization controller comprises a linear polarizer and fractional-waveplates, for instance a quarter-wave plate and a half-wave plate. Theseelements introduce wavelength-dependant non-orthogonality of the statesof polarization. Fractional-wave plates of the true-zero order type canbe used, which are characterized by reduced wavelength dependence.However, as any fractional-wave plate, they are designed for a givenwavelength, referred to as their optimized wavelength λ_(c). Whenmeasuring the polarization properties at wavelengths around λ_(c), thereis no need to compensate since the fractional-wave plates do notsignificantly disturb the orthogonality of the states of polarization.However, when operating at other wavelengths, the plates inducenon-orthogonality that cannot be overlooked and must be compensated for.

[0019] By way of example, in the case of fractional-wave platesoptimized around λ_(c)=1540 nm, the orientations shown in Table 1 beloware used to generate the four desired states of polarization at thewavelength λ 1540 nm. TABLE 1 Orientation of Orientation of Orientationof the Polarization state the polarizer the λ/4 plate (α) λ/2 plate (γ)Linear horizontal β β + 0° β + 0° Linear vertical β β + 0° β + 45°Linear 45° β β + 0° β + 22.5° Right-hand β β + 45° β + 0° circular

[0020] The angle γ characterises the orientation of the half-wave platewith respect to the polarizer, while the angle α characterises theorientation of the quarter-wave plate with respect to the polarizer.

[0021] When measuring at a wavelength other than optimal wavelengthλ_(c) of the fractional wave plates, it is possible to compensate forthe non-orthogonality induced by the retardation plates by a judiciouschoice of the angle γ of the half-wave plate and of the angle α of thequarter-wave plate. An example of a set of orientations for carrying outmeasurements around 1520 nm instead of 1540 nm which is the optimizedwavelength of the fractional-wave plates is given in Table 2 below:TABLE 2 Orientation of Orientation of Orientation of Polarization statethe polarizer the λ/4 plate (α) the λ/2 plate (γ) Linear horizontal ββ + 0° β + 0° Linear vertical β β + 0° β + 44.3° Linear 45° β β + 0° β +22.0° Right-band β β + 46.2° β + 0° circular

[0022] However, this type of compensation requires defining a referenceeach time the measurement is needed at a different wavelength, which canbe time-consuming. Furthermore, this type of compensation does not takeinto account the variations that occur inside the wavelength range ofmeasurements.

[0023] In order to be able to test more than one DUT at a time, and forpower monitoring, an optical splitter is preferably used at the outputof the polarization controller. However, such an arrangement is notstraightforward since, on the one hand the Mueller method requires thatthe four states of polarization at the entrance of the DUT be orthogonalon the Poincaré sphere, and on the other hand optical splitters may notmaintain orthogonality of the states of polarization. This may be causedby the presence of PDL in the optical splitters themselves.

[0024] It has been found that the above effects induced by thenon-orthogonality of the states of polarization on the measurements ofPDL and IL can be compensated for in accordance with the presentinvention.

[0025] In essence, therefore, the invention provides a method ofobtaining accurate polarization dependent loss (PDL) and insertion loss(IL) measurement, taking into account every polarization perturbationhaving a transfer matrix in a line between generation of known states ofpolarization and a device under test (DUT), which comprises computingwithin a desired range of wavelengths the transfer matrix of eachpolarization perturbing element in the line between the generation ofknown states of polarization and the DUT, or the transfer matrix of allpolarization perturbing elements as a whole, and compensating for errorsintroduced along said line by said polarization perturbing elements, soas to obtain an accurate measurement of the PDL and the EL of the DUT.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026]FIG. 1 is a graph showing curves of PDL in dB versus wavelength innm, obtained without perturbations, with perturbations and withcompensation of the perturbations in accordance with the presentinvention; and

[0027]FIG. 2 is a graph showing curves of IL in dB versus wavelength inn, obtained without perturbations, with perturbation and withcompensation of the perturbations in accordance with the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0028] According to the present invention, compensation of the errorsintroduced along the line, from the generation of incident states ofpolarization to the point where the PDL and EL measurements are done,permits accurate PDL and IL measurements wtihin a range of wavelengths.The novel compensation method permits to accurately calculate the PDLand IL of an optical device within a desired range of wavelengths.

[0029] In a first embodiment, the compensation method disclosed is basedon the calculation or measurement of the transfer matrix of everyelement disturbing the orthogonality of the states of polarization inthe line between the point where the incident states of polarization aregenerated and the point where PDL or IL of the DUT is to be measured.

[0030] In terms of the matrix formalism introduced, equation (1) must becorrected to take into account all these polarization perturbations:

|S _(ij out) |=|m _(ij)||perturbation₁||perturbation₂ |. . . |S_(ij in)|  (6)

[0031] where, |perturbation₁||perturbation₂|etc . . . are the transfermatrices of each polarization-perturbing element. These include thetransfer matrix of the fractional-wave plates of the polarizationcontroller when used at a wavelength different from their optimizedwavelength. Furthermore, in the event that an optical splitter is usedat the output of the polarization controller, the transfer matrix,referred to as [S_(canal-n)(λ)], of each one of the n channels of theoptical splitter is calculated. This wavelength-dependent matrix isincluded in the product of matrices defining the polarizationperturbations in equation (6). Thus, an accurate DUT transfer matrix|m_(ij)| is obtained by solving the equation (6) as opposed to equation(1) where no polarization errors are included. Consequently, thetransmission coefficients t_(j) are also accurately computed, allowingthe accurate determination of the PDL and the IL of the DUT by means ofequations (2) to (5) and (6).

[0032] In a second embodiment, instead of characterizing the transfermatrix of every polarization-perturbing element in the line for eachwavelength in the desired wavelength range of measurement, it ispossible to measure the output states of polarization at each wavelengthin said range of measurement with a polarization analyzer for any fourinput polarization states provided these are four independentpolarization states. That method amounts to considering the followingrelation between the input polarizations |S_(ij in)| and the measuredoutput polarizations |S_(ij out)|:

|S _(ij out) |=|m _(ij)|[perturbations]|[S _(ij in)]|  (7)

[0033] where |m_(ij)| is the Mueller or transfer matrix of the DUT and[perturbations] is the matrix incorporating all thepolarization-perturbing elements taken as a whole.

[0034] Thus the transfer matrix |m_(ij)| of the DUT is computable withaccuracy. This second embodiment permits to obtain the polarizationinput independent equations for the terms of the first row of theMueller matrix and thereby allows to obtain a most accurate PDL and ILcalculation.

[0035] In a further embodiment, the relation (7) in used in order tocompute the states of polarization that must be inputted into the line(|S_(ij in)|) so as to obtain four orthogonal states of polarization atthe input of the DUT. Therefore, the matrix product of the matrix of theperturbations by so determined matrix |S_(ij in)| gives the orthogonalpolarization states at the input of the DUT, which directly allows thecalculation of the PDL and IL of the DUT according to equations (2) to(5).

[0036]FIG. 1 provides an illustration of the invention with reference toPDL measurement. In this figure, the plotted crosses provide a curve ofPDL in dB versus wavelength in nm for an ideal case of non perturbedpolarization states. The plot of triangles shows a response obtained ina real case where a preturbation of 0.15 dB is introduced by thepresence of a splitter on the line between the polarization controllerand the DUT, or by the use of a polarization controller withfractional-wave plates that are used within a range of wavelengthsdifferent by more than 50 nm from their optimized wavelength This lineis clearly outside of the ideal curve. Finally, a plot made with dotsproduces a compensated line in accordance with the method of the presentinvention which corrects the line with the perturbation into anessentially ideal curve.

[0037]FIG. 2 provides the same illustration for the measurement of IL asdone in FIG. 1 for PDL. Here again the crosses represent the ideal curveof IL in dB versus wavelength in nm obtained with non-perturbedpolarization states. The plot with triangles represents a curve with aperturbation by means of a splitter between the polarization controllerand the DUT, which has a PDL of 0.15 dB or due to fractional-wave platesin the polarization controller that are used within a range ofwavelengths different by more than 50 nm from their optimizedwavelength. Finally, the plot obtained with dots produces a linecompensated in accordance with the method of the present invention andwhich corrects the non-compensated line into an essentially ideal curve.

[0038] The invention is not limited to the specific embodimentsdescribed above, but obvious modifications may be made therein by thoseskilled in the art without departing from the invention and the scope ofthe following claims.

1. Method of obtaining accurate polarization dependent loss (PDL) andinsertion loss (IL) measurement, taking into account every polarizationperturbation having a transfe matrix in a line between generation ofknown states of polarization and a device under test (DUT), whichcomprises computing within a desired range of wavelengths the transfermatrix of each polarization perturbing element in the line between thegeneration of known states of polarization and the DUT, or the transfermatrix of all polarization perturbing elements as a whole, andcompensating for errors introduced along said line by said polarizationperturbing elements, so as to obtain an accurate measurement of the PDLand the IL of the DUT.
 2. Method of obtaining accurate polarizationdependent loss (PDL) and insertion loss (IL) measurement, taking intoaccount every polarization disturbance having a transfer matrix in aline between generation of known states of polarization and a deviceunder test (DUT), which comprises computing within a desired range ofwavelengths the transfer matrix of each polarization perturbing elementin the line between the generation of known states of polarization andthe DUT using the following equation: |S _(ij out) |=|m _(ij) ||S_(ij in) | in which |m_(ij)| is the transfer matrix of DUT, |S_(ij out)|is the output polarization matrix of each element, and |S_(ij in)| isthe matrix of input state of polarization of each element, andcompensating for errors introduced along the line by said polarizationperturbing elements by correcting the above equation as follows: S_(ij out) |=|m _(ij)||perturbation₁||perturbation₂ | . . . |S _(ij in)|wherein |perturbation₁|, |perturbation₂| . . . are transfer matrices ofeach polarization perturbing element, thereby obtaining an accuratemeasurement of the PDL and the IL of the DUT.
 3. Method of obtainingaccurate polarization dependent loss (PDL) and insertionloss (IL)measurement, taking into account every polarization disturbance having atransfer matrix in a line between generation of known states ofpolarization and a device under test (DUT), which comprises computingwithin a desired range of wavelengths, the transfer matrix of allpolarization perturbing elements as a whole in the line between thegeneration of known states of polarization and the DUT, using thefollowing formula: in which |m_(ij)| the transfer matrix of DUT,|S_(ij out)| is the output polarization matrix of each element, and|S_(ij in)| is the matrix of input state of polarization of eachelement, and compensating for errors introduced along the line by saidpolarization perturbing elements by correcting the above equation asfollows: |S _(ij out) |=|m _(ij)|[perturbations]|S _(ij in)|  (5) where[perturbations] is the matrix incorporating all the polarizationperturbing elements taken as a whole, thereby obtaining an accuratemeasurement of the PDL and the IL of the DUT.
 4. Method of obtainingaccurate polarization dependent loss (PDL) and insertion loss (IL)measurement by first determining the state of polarization that must beinputted into a line leading to a device under test (DUT), so as toobtain four orthogonal states of polarization entering the DUT, and thencomputing within a desired range of wavelengths the transfer matrix ofeach polarization perturbing element in the line between the inputtedstates of polarization and the DUT and compensating for errorsintroduced along said line by said polarization perturbing elements, soas to obtain an accurate measurement of the PDL and the IL of the DUT.5. Method of obtaining accurate polarization dependent loss (PDL) andinsertion loss (IL) measurement by first determining the states ofpolarization that must be inputted into a line leading to a device undertest (DUT), so as to obtain four orthogonal states of polarizationentering the DUT, and then computing within a desired range ofwavelengths the transfer matrix of all the polarization perturbingelements as a whole in the line between the inputted states ofpolariztion and the DUT, and compensating for errors introduced alongsaid line by said polarization perturbing elements, so as to obtain anaccurate measure of the PDL and the IL of the DUT.
 6. Method accordingto any one of claims 1 to 5, in which the polarization perturbingelements include fractional-wave plates of a polarization controllerused to perform required measurements.
 7. Method according to any one ofclaims 1 to 5, in which the polarization perturbing elements include anoptical splitter located at the output of a polarization controller usedto perform required measurements.